The number of bacterial colonies per cubic centimeter in a certain polluted lake is assumed to be

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The number of bacterial colonies per cubic centimeter in a certain polluted lake is assumed to be Poisson distributed with parameter \(\lambda\). You sample 1 deciliter, and find 157 bacterial colonies. Use neutral prior, and test the alternative hypothesis \(H_{1}: \lambda<1.75\) with significance \(\alpha=0.04\).

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